Ring charge This was left as an exercise. Consider the following ring of charge with radius R and total charge Q. Show that the expression (or the integral) for the electric field at point P is given by

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Chapter1: Units, Trigonometry. And Vectors
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Ring charge This was left as an exercise. Consider the following ring of charge with radius R and
total charge Q. Show that the expression (or the integral) for the electric field at point
P is given by
Ez
=
R
kQz
(2²+R²)³/2
r
E.
Disc charge Now let's see how we can use the above result to find the electric field due to a charged
disc. Typically for a disc you would need to evaluate a 2D integral, but if you image
the disc as an accumulation of ring charges, the integral is effectively 1D¹.
Ep
P
R
Z
O = area charge
density
R
dR'
¹Hint: Think about how you would express dQ = odA can be expressed in terms of dR, i.e. how would
A and R relate (hence dA with dR).
Transcribed Image Text:Questions Ring charge This was left as an exercise. Consider the following ring of charge with radius R and total charge Q. Show that the expression (or the integral) for the electric field at point P is given by Ez = R kQz (2²+R²)³/2 r E. Disc charge Now let's see how we can use the above result to find the electric field due to a charged disc. Typically for a disc you would need to evaluate a 2D integral, but if you image the disc as an accumulation of ring charges, the integral is effectively 1D¹. Ep P R Z O = area charge density R dR' ¹Hint: Think about how you would express dQ = odA can be expressed in terms of dR, i.e. how would A and R relate (hence dA with dR).
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Given:ringhasradius,RpointPisrfromtheringandzfromcenteroftheringtotalchargeonthering,QAsked:ToshowthatelectricfieldEFatPisEz=kQzz2  +R23/2usethistoderiveEFatPduetoadisc.

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